Central tendency refers to identifying the central position of the given data set. Central tendency has 3 important measures hat are Mean, Median, and Mode. Students are several times confused between each of them. So here, we will explain the differences between all three of them with the help of examples.
Mean: Mean, here the arithmetic mean is the most used measure of central tendency. With both discrete and continuous data set, a mean can be obtained. To obtain the mean of a set of numbers, you have to sum up all the numbers and then divide it using the total numbers. In short, it is taking out the average of all numbers. It can also be said that it is the ratio of the sum of all observations to the total no of observations. In pre-primary classes, it was introduced as average to the students while in higher classes we came to know that it is also known as Mean.
Median: When you arrange a given set of numbers from smaller to biggest, the middle number is said to be the median. Arrange any given series in either ascending or descending order or the middle value then is termed as the median. To find the median the data can be arranged in either descending order or ascending order. In geometry, it is defined as the center or midpoint of a polygon.
Mode: The most repeated number in a given set of observations is the mode or it can also be said that the Number or Value which have the highest frequency in a given series of numbers. It is also known as the modal value. It is a part of 3 central tendencies apart from the median and Mean. It is the highest bar if presented in a histogram or a chart form. If there is no repeated number in a given series then no Mode will exist for that series.
Table of differences between Mean, Median, and Mode
All these measures of central tendencies are co-related. They share an empirical relationship but are different from each other. Here are the differences:
S.No | Mean | Median | Mode |
1 | The average taken of given observations is called Mean. | The middle number in a given set of observations is called Median. | The most frequently occurred number in a given set of observations is called mode. |
2 | Add up all the numbers and divide by the total number of terms | Place all the numbers in ascending or descending order | the mode is derived when a number has frequency occurred in a series |
3 | Once the above step is finished, what we get is the mean. | After arranging everything from smallest to biggest, take out the middle number, which is your median. | The mode can be one or more than one. It is possible to have no mode at all, as well |
4 | Mean is the arithmetic mean or in a simple way can be a simple average or weighted average. | When series have even numbers, median is the simple average of the middle pair of numbers. If there is a unique data set, there is no mode at all. | If there is a unique data set, there is no mode at all. |
5 | When data is normally distributed, the mean is widely preferred. | When data distribution is skewed, median is the best representative. | When there is a nominal distribution of data, the mode is preferred. |
6 | Mean= x̄ = ∑x/ N |
If the total number of observations (n) are odd then median is: Median = (n + 1/2)^{th }observation If the total number of observations (n) are even number, then the formula is given below: Median = (n/2)^{th }observation + (n/2+1)^{th }observation /2 |
The mode is the most frequently occurring observation or value |
Sample Problems on Central Tendency
Problem 1: We have a set of numbers that is 4, 8, 2, 1, 1, 4, 3, 1. Find the mean, median, and mode.
Solution:
Mean:
8 + 4 + 2 + 1 + 1 + 4 + 3 + 1 = 24 and 24/8 = 3
Median:
2 + 3/2 = 5.2 (after arranging the numbers in ascending order as 1, 1, 1, 2, 3, 4, 4, 8 and middle terms are 2 and 3 as total number of terms are 8 which is even)
Mode:
1 because it is present 3 times in the sequence
Problem 2: We have a set of numbers that is 4, 2, 1, 6, 5, 3, 7, 1, 10, 9, 8. Find the mean, median, and mode.
Solution:
Mean:
1+1+2+3+4+5+6+7+8+9+10 = 56 and 56/10 = 5.6
Median:
5 (after arranging in ascending order 1,1,2,3,4,5,6,7,8,9,10 the middle term is 5)
Mode:
1 {as it is repeated the highest number of times(2 times)}.